Final answer:
The leading term of f(x) is x^24, the degree of f(x) is 24 and the leading coefficient is 17. The end behavior corresponds to both ends of the graph going upwards.
Step-by-step explanation:
The correct answer is option Mathematics. To determine the end behavior of the polynomial function f(x) = 17(x − 3)15(3 − x)9, we need to look at the highest degree terms after simplifying the expression. Given the odd powers, multiplication will result in a leading term with the highest degree possible, being the combined sum of the degrees. Simplifying, we have a leading term of x24.
The leading coefficient is obtained by multiplying the coefficients associated with the leading term. Thus, 17 is the leading coefficient. The degree of the function is 24 because that's the sum of the exponents when the expression is fully multiplied out. For the end behavior, we observe that the degree is even and the leading coefficient positive, so both ends of the graph will go in the same direction, upwards.
The correct answer is option (a) y = 13x.
In the given polynomial function, f(x) = 17(x−3)¹⁵(3−x)⁹, the leading term is the term with the highest exponent. In this case, the leading term is (x−3)¹⁵, which has a degree of 15. The leading coefficient is the coefficient of the leading term, which is 17.
The end behavior of a polynomial function is determined by the leading term. Since the degree of the leading term is odd (15), the end behavior of the function is opposite: as x approaches positive infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches positive infinity.